Question

In which interval is the given function, f(x) = 2x³ - 21x² + 72x + 19 monotonically decreasing?

पर्याय

• [3, 4]

• (3, 4)

• (-∞, 3)

• (4, ∞)

Answer 1

(3, 4)

Explanation:

f(x) = 2x³ - 21x² + 72x + 19

∴ f'(x) = 6x² - 42x + 72x

= 6(x² -7x + 12)

= 6(x - 3)(x - 4)

To be monotonic decreasing, f'(x) < 0

⇒ (x - 3)(x - 4) < 0

⇒ x ∈ (3, 4)